Grace Tutorials

Edward Vigmond evigmon@tulane.edu for Grace-5.1.4

Contents

1 Introduction 2 1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Computer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Disclaimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Making a Simple Graph 4 2.1 Reading the data from a file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Set appearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Colouring all sets differently . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Customizing each set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Labelling the axes using the font tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Graph titles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.5 Legends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.6 A challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Block Data 6

4 Creating sets within Grace 6 4.1 By formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 In spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 In text editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.4 From block data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Batch plotting 8 5.1 Simple nonGUI printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.2 Multiple graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5.2.1 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.3 Things for which no command line option exists . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.3.1 Pexec example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.3.2 Batch example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6 Fitting curves 10 6.1 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 6.2 Non-linear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7 Transformations 11

7.1 Graphical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 7.1.1 Simple Geometrical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 7.1.2 Mathematical operations between sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 7.1.3 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

7.2 Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7.2.1 Defining a region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7.2.2 Using regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8 Using Pipes 13 8.1 Instead of data files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 8.2 Named pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

9 Multiple Graphs 14

9.1 Selecting graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 9.1.1 Arranging a tableau of graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 9.1.2 Arranging individual graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9.2 Overlaying Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

10 Hot Links 16 10.1 File containing a Single Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 10.2 Multiple sets within a file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 10.3 Updating by hot keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1 Introduction

These tutorials assumes that you are a new user to Grace but are somewhat familiar with a windowing system. They are designed to show you some of the basic operation of Grace as well as a few of its less intuitive features. Please feel free to go beyond the bounds of the actions described herein and explore the possibilities of using Grace. After all, you will be the one who benefits.

1.1 Purpose

The purpose of these tutorials are to give brief examples to show you the basics of how to do something. Essentials and some of the more esoteric features of Grace will be demonstrated to give the user an idea of the capabilities of this program. It is not possible to show everything that Grace is capable of doing. That knowledge only comes with use and experimentation. I recommend that you do the tutorial and then by playing around with things, you will begin to understand them. Finally, when you get stuck, read the user guide to help you.

1.2 Nomenclature

In referring to what item to select, the tutorial will use something of the form snaf:/foo/bar/bell which means that on the snaf popup, select from the foo menu the submenu bar and from the bar menu, the entry bell. The popup main is the large one with the graph that pops up when you run xmgrace. If there is a space in the menu item, it will be replaced by an underscore. So , if the menu item was actually ”Bell jar” instead of bell in the last example, it would be snaf:/foo/bar/Bell jar.

Things that are to be typed in will be presented in a typewriter font, eg, type y = 3*sin(x).

Some of examples require you to input a data file or graph. In such instances, there should be a file in the tutorial directory named data.N or N.agr where N is the tutorial number. For example, when doing tutorial 7.1.3, you should look for a file 7.1.3.agr. It is assumed that each major tutorial section starts with a clean graph.

1.3 Computer System

Some of the following examples require that system commands be run. The commands may be different on your machine or require a slightly different syntax. In this tutorial, an attempt will be made to use the most commonly available UNIX commands. This tutorial was prepared on a Linux machine with kernel 2.0.32.

1.4 Generalities

A couple of points should be made about the GUI before we begin to make life easier.

1. It is often possible to select more than one item from a list at a time (some lists may prevent it when it makes no sense.). Clicking on a list entry without any keyboard modifier pressed will deselect all other entries and select only that one. Depressing shift while clicking an entry selects all entries from a previously selected entry to the currently selected one. Finally, depressing control allows one to individually toggle the selection of an entry.

2. There are often two buttons on a pop up: Apply and Accept. Changes are not registered until either of these buttons is pressed. The difference between them is that Accept also closes the window.

1.5 Disclaimer

Even though I do my best to keep this up to date with the latest release, I cannot guarantee it. Think of this a perpetual work in progress. Therefore, if something is wrong, you can notify me and I’ll fix it but keep in mind that I am doing it in my spare time for no money.

2 Making a Simple Graph

The object of this tutorial is to do the most basic function of Grace: read in some data into a graph and then label the graph. Along the way, a few of the basic Grace commands and widgets will be introduced.

2.1 Reading the data from a file

Start by bringing up the set reading widget Main:Data/Import/ASCII . Select the file 2.1.dat (both double clicking and hitting return work). You should see a black curve drawn on a graph.

Now we would like to add some more sets to the graph, but this time the data file will be in a slightly different format. Looking at the file ”2.1.dat” (with the program of your choice), you can see that its several columns of numbers. One way to interpret this file is the first column gives the x-values and the rest of the columns are y-values. From Grace, again open the ”Read Sets” widget. This time, check the ”NXY” button. Now select the file ”2.1.dat”. At this point you will have several differently coloured curves.

You should now have 2 copies of the first set since you’ve read the file twice. It would be nice to eliminate one copy. This is most easily accomplished by bringing up a popup which lists all the sets. Selecting Main:Edit/Data sets...bring up the Data set props popup. It lists all the sets and for the selected set, its type and a few statistics. To eliminate a set, select it and then press the right mouse button. A menu should appear from which you can select kill. You’ll note that there is a kill and kill data. The former totally eliminates everything associated with a set while the latter eliminates the data but keeps the settings for it so that if new data is read into the set, it will have the same properties like colouring and line width, etc. Kill set 0 for now.

2.2 Set appearance

We would now like style the sets. Practically all aspects of the curves are configurable including colour, line thickness, symbols, drop lines, fills, etc. These operations are available under the ”Set appearance” widget which is invoked by selecting Main:Plot/Set appearance... or by double clicking near the target set within the graph frame.

When the widget comes up, there will be a list of the sets with their number (eg. G0.S1 refers to set 1 in graph 0). Later operations will require you to know the number. Like the data sets pop up, clicking on mouse button 3 in the set list will bring up the menu of set operations.

2.2.1 Colouring all sets differently

The simplest way to colour all sets differently is from Set Appearance:Data/All colors. First select the sets which you wish to recolour and then select Set Appearance:Data/All colors. Do this now to your graph.

2.2.2 Customizing each set

When a set in the list is highlighted, the widgets change to reflect the settings. Practically all aspects are configurable. Experiment by changing the line colours and widths, placing a symbol at each data point, not connecting data points and fill the space between the x-axis and the curve. Don’t forget to try out what is available under the other tabs besides Main. To see the effect of a change, you have to hit the ”Apply” button. N.B.: Things are drawn in numerical order so if there is overlap, the highest numbered item will be on top. This applies to graphs and sets within each graph.

2.3 Labelling the axes using the font tool

Aspects of the axes are controlled by the axes popup which is called from Main:Plot/Axis properties or by double clicking the graph frame. All aspects of the axes can be changed like the title, the font, colour, whether or not to draw grid lines, or user defined tick marks and labels. There are many settings and the best thing to do is to experiment to see what each setting does.

For now, let’s start by labelling the axes. Suppose these curves represent the number of tasks a processor runs as the function of the number of users. To make it more interesting, assume we are doing this in Quebec. That means we want to plot ”Nombre de tâches vs. nombre d’usagers”. Note the importance of having the accent over the a in tâches or we would end up plotting the number of stains which is entirely another case. Bring up the Axes pop up, select the Y axis, and click in the space to enter the label string of the axis label. Start typing Nombre de t. At this point we need to enter a accented letter, so we bring up the font tool by pressing Control-E. You will now see what we have typed in the Cstring widget. Move the cursor to where you want to place the accented letter and click on the letter. It should now appear in the string. You can either finish the string here or hit accept and keep editing. Label the x axis as well. This font tool is available wherever text needs to be entered.

All the attributes regarding the axis labels like size, colour, font, position are changeable.

2.4 Graph titles

Our next exercise will be to title the graph so other. Operation pertaining to this are found in the ”Graph appearance” widget which we open by selecting Main:Plot/Graph appearance or by double clicking just above the graph frame.

We can now fill in the title of the graph and by clicking on the ”Titles” tab, the font and size and colour can be chosen. The Viewport box under the ”Main” tab defines the 4 corners of the graph frame. You can type them in or use the mouse to move them by first double clicking on them.

Other things which can be controlled in this widget are the frame drawn around the graph, whether or not the graph background is coloured and the legends. Legends will be dealt with a little later.

2.5 Legends

Since we have several lines in our graph, it makes sense that we label them with a legend so that other people can figure out what they mean. The first thing to do is to give each set a label. This is done by entering a legend string for each set in the Set appearance popup. Now, from the Main form in the Graph appearance popup, click on ”Display legend” to see the legend box. The location and appearance of the box is controlled by clicking on the ”Leg. box” tab. The appearance and spacing of the legend entries is controlled by the ”Legends” tab. For simplicity, label the sets alphabetically and then play with the appearance, etc. to get something you like.

Specifying the placement of the graph by entering the coordinates can be painful, especially the fine tuning. To alleviate this problem, a graphical method is also available, although not readily apparent. After a legend appears, it may be dragged to a new location. To do this, press Ctrl-L with your mouse on the main canvas. You should see the arrow cursor turn into a hand. If this doesn’t work, double click on the main canvas (to get its attention) and then press Ctrl-L. Click on the legend and drag it. To cancel the legend drag mode (as with all other modes), click on mouse button 3.

2.6 A challenge

I got bored so I took the data files and produced my own, albeit ugly, graph. See if you can copy mygraph.png

3 Block Data

A block of data is a table of number which are interpreted as columns of numbers. How sets are created from the columns depends on the information you want to extract from the file.

We first need to read in a block of data. We do this from Main:Data/Import/ASCII . Select the file ”3.dat” and Load as ”Block data”. If the read was successful, a window should pop up asking you to create a set from the block data. At the top it will list how many columns of data were read.

First we choose the type of set we would like. For now we’ll stick with xy.

Next we choose which column of data contains the x-ordinate. If there is no column, we can select ”index” which will use the index into the column as the x ordinate starting from one.

The values Y1 through Y4 are used for selecting error bars as may be needed by other set types.

The last thing to specify is the graph into which to load the set if we have more than 1 set.

Finally, hitting accept will create the set.

If you close this window, it can reopened by bringing up a set list (eg. Main:Edit/Data sets) and then selecting Create new/From block data from the menu brought up by right clicking on the set list.

Try creating a new set of type XYdY. This is an XY curve with error bars. Try X, Y, and Y1(the error) from different columns.

4 Creating sets within Grace

Besides reading in data files, Grace has an extensive scripting language with a large number of math functions built in, These function include the basic add, multiply, square root, etc, and also the cephes library of higher order math functions like Bessel functions and the gamma function. Hence, functions in Grace are basically unlimited. See the user guide for more details. In addition, users can dynamically add libraries to Grace with any desired function. As well, points may be added manually to a set by the use of editors. To begin, choose Main:Edit/Data sets. To create a set, press mouse button 3 (the rightmost one for right handed people) anywhere within the data set list (which may be empty) and select Create new. A menu with 4 different ways of creating new sets will be presented. We’ll go through them one by one.

4.1 By formula

The load and evaluate window will pop up when this is selected.

1. The first step is to set up the parameter mesh which will determine the range and sampling of the variable $t. Most often, $t will simply be the abscissa.

2. Next, choose the type of set you would like to produce.

3. Using the syntax of the command language, an expression for x is entered which uses $t as the independent variable. This can be an extremely complicated function.

4. Likewise, an expression for y is entered and for any other expressions that may be needed. Fields after y are labelled y1, y2, y3 and y4. For example, if the set type xydxdy is chosen, y1 will hold dx and y2 will hold dy and it will be necessary to enter expressions for them.

5. Pressing apply or accept will perform the calculations and create the new set. You may have to autoscale to see the new set.

Below are a few samples:

1. To plot one cycle of a sine wave: Load: Set X, Start load at: 0, Stop load at: 2*pi, Length: 100,

     X=$t, Y=sin($t)

2. A unit circle by parameterization: Start at:0, Stop at: 2*pi, Length: 100, X=cos($t), Y=sin($t)

4.2 In spreadsheet

If your system has the Xbae widget set, this choice brings up a spreadsheet like editor to allow one to enter the points of the set by hand. Initially, it just has the point ( 0, 0 ). Clicking on add will insert a copy of the currently selected row immediately below the selected row. Clicking delete will delete the row which contains the cursor. This method is best suited to examining or modifying existing sets or creating very small sets. The sets gets updated after one hits enter or leaves the cell.

4.3 In text editor

If your system doesn’t have the Xbae widget set or you want the power of your favourite external editor, a text editor of your choice may be used to enter data. The editor is selected by the GRACE EDITOR environment variable. If the set is new, it will contain only the point (0,0). During editing, no other operations are possible. After the editor is closed, the set will be updated.

4.4 From block data

This creates a new set from a block of data which has been read in. See section 3.

5 Batch plotting

Grace supports a large number of command line options which allow the user to control the appearance and placement of graphs. This can be very useful if you want to use it to quickly print something without going through the GUI, use it within a script to automatically generate graphs, or have a plot come up already configured which can be much quicker than going through the GUI menus.

5.1 Simple nonGUI printing

Invoking Grace with the command ”grbatch”from the command line will cause Grace to start, produce a plot, send it to the printer (unless a file is specified) and then exit. In its simplest form, to produce a plot of the file a.agr, type

gracebat a.agr

If gracebat is unavailable on your system, the hardcopy option to xmgrace will do the same thing. Assuming the hardcopy device is a postscript printer, one could also type

xmgrace -hdevice PostScript -hardcopy a.agr

5.2 Multiple graphs

Often, one wishes to plot several graphs with each graph having different characteristics. This is easily accomplished from the command line. Options specified on the command line are parsed in order and stay in effect until overridden by specifying them again.

1. The first step in plotting multiple graphs is usually telling Grace how many graphs we have and how to arrange them. The interpreter command ”arrange” will do this. For example, if we want 4 graphs arranged in a simple 2x2 table, we specify -pexec ”arrange ( 2, 2, .1, .1,.1,ON,ON,ON)” The exact meaning of all the options is explained in the reference manual.

2. Specify any global options.

3. Specify for each graph, the data to plot and any options. Options should be specified in the following order:

(a) ”-graph g” where g is the graph number starting at 0. This says to apply all following options to this graph.

(b) Set any autoscaling options. Autoscaling is performed when the file is read; ergo, the autoscaling must be specified BEFORE the file is read. Remember, this setting is persistent.

(c) Set the set type. This is also a persistent setting.

(d) Specify the graph type and the input file.

(e) If reading in block data, create the sets with the ”-bxy” option.

(f) Specify any world scaling. It is important to do this AFTER sets are read (unless autoscaling is off) as the graph gets rescaled when data is read in.

(g) Specify anything else 5.2.1 An example

Let’s try an example. We will assume 5 plots, the first 4 of which are to be stacked vertically, and the fifth inset into the fourth. We wish to plot the files a.dat, b.dat, c.dat and d.dat with the inset graph being a magnified portion of d.dat. Assume a.dat contains multiple columns of data, b.dat is a block of data from which we wish to make a curve from columns 2 and 4 with the error given by column 3, c.dat is to be represented as a bar graph, and for the inset graph, we wish to graph to region (0,0) to (1,1). This can be accomplished by

gracebat -pexec ”arrange (4,1,.1,.1,.1,ON,ON,ON)” -nxy a.dat -graph 1 -block b.dat -settype xydy -bxy 2:4:3 -graph 2 -settype bar c.dat -graph 3 -settype xy d.dat -graph 4 d.dat -world 0 0 1 1 -viewport .15 .3 .8 .88

Note that the graph numbers start at 0 and that 0 is the default so it does not have to be specified for the first graph.

5.3 Things for which no command line option exists

Undoubtedly, you will reach a point where you want to do something for which no command line option exists. (We have been doing this with the arrange command.) This is where Grace’s parameter file language is vital. The option ”-pexec” will execute the next argument as if it had read it from a parameter file or excuted on the command line. If you want to do something more complicated than one command, you can use several pexec’s or put the commands in a file and run the file with the ”-batch” option.

5.3.1 Pexec example

To read in the files foo.dat and bar.dat and scale foo.dat in Y by 1000, the simplest way is

xmgrace foo.dat bar.dat -pexec ”s0.y = s0.y * 1000”

5.3.2 Batch example

To do the same as the previous example but also label the axes and recolour the curves, make a file called ”bfile” with the Grace commands

#Obligatory descriptive comment
s0.y = s0.y * 1000
s0 line color 3
s1 line color 4
title "A Gnasty Graph"
xaxis label "Time ( s )"
yaxis label "Gnats ( 1000's  )"
autoscale

and then run xmgrace with

xmgrace foo.dat bar.dat -batch bfile

6 Fitting curves

This tutorial will explain some of Grace’s curve fitting abilities. Grace can perform two types of fittings. The first type is regression or linear fitting where optimization is done on a linear equation or an equation which can be expressed in a linear form. This includes fitting polynomials and certain forms of equations. The other type of fitting is nonlinear and allows for arbitrary user supplied functions.

Let’s take a curve and see how each type of fitting works. To begin, create a curve of the function y = sqrt(x) + exp(x)/3 -1 over the range 0 to 3 with 100 points.

6.1 Linear Regression

Choosing Main:Data/Transformations/Regression will pop up the Regression window.

1. Select the set you just created

2. Select the type of fit. For now, pick Linear.

3. We will load the fitted value for now.

4. Press the accept button to see the results of the fit. A window will pop up which will give you the results of the fit including the final expression. You might have to scroll back a bit to see it.

5. See how high of a polynomial is needed to get an acceptable fit and try fitting other types of functions. Note that for the non-polynomial fits, A and B are the fitting parameters of the equation.

6. Now, we are not limited to computing our fitted curve at the points of the original function. Suppose these data are quarterly sales and we wish to predict our next quarter. Choose the type of fit which you found to work best. Instead of loading fitted values,Load: Function. Now the bottom of the widget will become active. We wish to extrapolate over the next quarter, so we would like to start at 0 and end at 4 and choose 100 points. Press accept to see the extrapolation.

6.2 Non-linear

We pop up the widget by selecting Main:Data/Transformations/Non-linear curve fitting. You may want to kill all the sets except the original function and the extrapolated function at this point.

1. Begin by selecting the set to optimize, the original function.

2. Next, we write a function of the form we wish to fit. The unknown parameters are labelled a0..a9. You must start with a0 and work your way up. In this case, since you know the form of the equation

     already, so try: y = a0*sqrt(x) + a1*exp(x) + a2.

3. Next we must specify that we have three parameters to fit which are a0, a1 and a2 and the tolerance of the solution.

4. You must specify initial values for the parameters and put any bounds on them if necessary. Depending on the function you are optimizing, different initial conditions may lead to drastically different optima.

5. The solution process is iterative and you must click on a button to run a certain number of iterations. You should see the parameters change and a curve created with these parameters. In this example, the exact solution is reached within 5 steps. More parameters and more difficult functions may require more steps in which case you may choose to run 20 or 100 or more steps. The newly created optimized curve should converge with an increasing number of steps.

6. As in linear curve fitting, you can choose to load the fit function at the points of the original curve, over an arbitrary range or load the error at each point. For comparison, load the fitted curve over the range (3,4) by selecting Nonlinear:Options/Load/Function and filling in the bottom of the widget. How does the true answer compare to your previous extrapolation?

7. Fitting arbitrary curves can be a tricky business. Initial conditions are very important. If you don’t get a good fit, you may have to experiment a lot with the initial parameters values.

8. Finally, note that the fitted curve does not get added until the accept button is pressed. This allows you to ”fool around” until you get a good fit without creating a lot of garbage sets.

7 Transformations

7.1 Graphical

7.1.1 Simple Geometrical

You can rotate sets around an arbitrary axis perpendicular to the canvas (e.g. the Z-axis). Also it is possible to scale sets and translate them.

7.1.2 Mathematical operations between sets

It is possible to perform operations between sets. With many operations, however, it is required that the 2 sets have the identical abscissa, i.e., the x values of both sets are the exact same. This is necessary since most operations are performed on a point by point basis. Eg. multiplying 2 sets is done by multiplying the Y values of the 2 sets together to produce a new Y value. About the only operations that don’t do this are filtering and convolution. Fortunately, Grace has a function to help out when the abscissas differ. It is called interpolation which interpolates a set over the domain of another set to produce a new curve.

Let us now add the cosine of a set to the sine of another set to create a new curve. However, we will complicate this example by having different domains with different sampling:

1. Read in 7.1.2.agr

2. Note how the abscissa are different. We begin by using interpolate to produce a third set which is the second set sampled at the x values of the first. Call up the Interpolate popup from Main:Data/Transformations/Interpolation/splines ...

3. Select S1 as the source set but don’t specify a destination set. A set will automatically be made. Use the Strict, linear method, Sampling:Abscissas of another set and use S0 as the Sampling set. Pressing Apply should produce a curve which is S1 interpolated at the points of S0. Note that the new curve only exists over the portion of the x axis common to both curves.

4. We still have a problem since set 2 is sampled the same as set 0 but has a smaller domain. We can perform the computation only over the common region so we now interpolate on set 0 at points from set 2 to produce set 3. Now set 2 and set 3 have the exact same abscissas.

5. Call up the command interpreter from Main:Window/Commands ...

6. We need to create a set to hold the result, S4. We can either make a copy (using Main:Edit/Set operations...) of S2 which will be guaranteed to have the proper size to hold out result or we can use type a command: s4 length s2.length

7. We have to break up the computation into an x part and a y part. In this instance, we simply wish to keep the same x values. The final result will be put into set 4, so we issue the command: s4.x = s2.x

8. Now we can perform the math between our interpolated copies of sets 0 and 1: s4.y = cos(s3.y) +

sin(s2.y).

9. So where is the new set? It’s there but it’s hidden. Since we already have the command window open, we can unhide the set by typing: S4 on. For the GUI minded (no offense intended), bring up a set list with the set operations menu (eg. Main:Edit/Data sets or Main:Plot/Set appearance), select set 4 and unhide it by selecting show from the operation menu (mouse button 3).

N.B. If the abscissas of the original curves had been the same, we could have started at step 5. If the sampling had been the same we could have skipped step 4.

7.1.3 Feature extraction

Feature extraction is a way of creating one curve from a family of curves. It generates one data point from each curve by measuring a characteristic of the curve. For example, one might have a series of curves which plot the gnat population as a function of time. Each curve is produced by varying some condition, like the number of gnus in the environment. Using feature extraction, one could use this family of curves to produce a new curve of the peak number of gnats as a function of gnus or the time of the peak number of gnats as a function of the number of gnus. This is most often useful with more than one graph.

1. Read in graph 7.1.3.agr

2. Bring up the feature extraction form by clicking on Main:Data/Transformations/Feature extraction.

3. Select Results to graph 1.

4. Select the feature you are interested in. Choose Y maximum.

5. Select what will determine the x value of the data point. The value of the characteristic determines the Y value. The X value can be determined by the set number. The x or y values of a specified set can also be used to produce the abscissa. Finally, the legend entry of the curve itself can be used to produce the x value. In this case, the legend entry must be specified as a single number. Choose index for now.

6. Press accept, click on graph 1 and then click on the autoscale button to see your results.

7. Choose another feature, like frequency, this time and get X values from the legend. Make sure that graph 0 has the focus when you hit accept.

7.2 Restrictions

Often we only wish to examine part of a data set or perform transformations only on a portion of one. Restrictions allow us to define a region of the graph on which to perform operations.

7.2.1 Defining a region

There are several ways a region may be defined. It may be defined by a straight line (left of, right of, above, below), by a polygon (inside or outside), or by a range ( in x, out of x, in y, out of y). Call the define region popup from Main:Edit/Regions/Define. Choose which one of the regions you would like to define, and press the define button.

Line type Define the ends of the line by clicking with mouse button 1.

Polygon type From the define region popup, choose a polygon type and then the define button. Use mouse button 1 to pick the vertices of the polygon and then mouse button 3 when you are done.

Range type From the define region popup, choose a range type and then pick 2 points which define the range.

7.2.2 Using regions

Regions may be only be used to restrict an expression evaluation. Bring up the evaluateExpressions popup (Main:Data/Transformations/Evaluate expression). Choose the source and destination sets and specify the formula to apply to the region of interest. Not specifying an expression is equivalent to the identity transformation. Choose the region you wish to use. By checking negate, the complement of the specified region is used.

Click on Apply to perform the operation. The resultant set will be the expression evaluated only on points contained in the specified region. Thus, if no expression was specified, the effect is to produce a new set of only those points contained in the region. Conversely, to delete points in a region, leave the expression empty, and negate the region selection.

8 Using Pipes

Pipes are a way of capturing the output of a running process without the intermediary step of pacing the output in a file. Instead, the executing program puts the data in one end of the pipe, and Grace reads it from the other end of the pipe.

8.1 Instead of data files

On certain popups, e.g. Main:Data/Import/ASCII , the option to read from a file or pipe can be specified. If a pipe is chosen, the command in the selection widget will be run and the stdout will be captured and treated as though it was data which was read from a file.

8.2 Named pipes

A named pipe is a special case of the pipe previously described. In the previous case, after the program has finished execution and the output had been read, the pipe was destroyed. A named pipe is a static structure with the property that multiple processes can write to and/or read from it. The purpose of using a named pipe with Grace is to start up a Grace window and then control Grace by sending commands and data through a named pipe. This is very powerful and lets you do practically anything you can do directly from the GUI. To use this feature, try the following:

1. Start a named pipe (you will have to find the command specific to your operating system. For example, it could be mkfifo or mknod): mkfifo pvc. If you do a directory listing, you should see the file pvc.

2. Start up Grace in the background using the named pipe option: xmgrace-npipepvc&. Grace is now monitoring the pipe for any data which might be sent to it. It will interpret things as though they were entered using the command interpreter.

3. For a simple test, we will create a simple graph over the pipe. From your command line, type: echo "read \"8.2.dat\"" > pvc. (The back slashes are needed to escape the quotation marks so that Grace really received the command :read ”8.2.dat”.) This just told Grace to read the file data. Now we would like to autoscale. We could simply click on the button but the point is to use a named pipe. This time we type echoautoscale > pvcfollowed byecho redraw > pvc. Your graph should now have autoscaled and redrawn. Exit Grace with echoexit> pvc. You should also clean up by removing pvc.

4. The true power in named pipes lies in driving Grace using another program. The controlling program can open a named pipe for writing, which is treated as an ordinary file. It can be opened with the fopen() function or whatever other I/O function you prefer. Commands and data are then written to the file where they are interpreted by Grace.

9 Multiple Graphs

9.1 Selecting graphs

When multiple graphs are present, a graph is selected by clicking inside the graph frame. In cases where graph frames overlap, clicking will cycle among the overlapping graphs.

It might be annoying if one is trying to work in a region of overlapping graphs. If will not be possible to double click on something because the each click will be interpreted as a single click and you will only end up changing the graph focus. In such an instance, turning off the graph selection by clicking might be desirable. Choose Main:Edit/Preferences and then set Misc:Graph focus to ”As set”. This means one must explicitly set the focus. Simply bring up a graph list (eg. Main:Edit/Overlay graphs is but one), select the graph you want to work on and then, using the menu under mouse button 3, choose ”Focus to”.

9.1.1 Arranging a tableau of graphs

Placing a large number of regularly spaced graphs is easily done with Main:Edit/Arrange graphs. This will automatically calculate the layout:

1. Choose 3 rows and 3 columns and Apply. You should now see 9 graphs. The Order button refers to the way the graphs are numbered. The beginning of the line on the diagram of the button shows which graph is numbered 0 and how the numbers increase, by row or column.

2. You realize you need horizontal packing, i.e. no horizontal gap between graphs. Click on the Pack button beside the Hgap/width input and then Apply.

3. Suddenly, you realize you only need 6 graphs and not 9. Choose 2 rows and press Apply. There is a slight problem as graphs 6, 7 an 8 are still visible. This is a feature since you don’t want to accidentally kill a graph. You can kill the extra graphs by clicking on the ”Kill extra graphs” check box. Now, any graphs other than the explicitly arranged ones will be automatically killed.

4. The margins are controlled by the Page Offsets, and the intergraph spacing by the Hgap and Vgap inputs.

5. Press close to remove the window.

Note that only graphs which are selected are taken into consideration. So, if you wish to reorganize your existing graphs, make sure they are selected or new ones may be created.

9.1.2 Arranging individual graphs

Arranging individual graphs may either be done (1) exactly, by specifying the viewport coordinates from Main:Plot/Graph appearance or using the previously explained Arrange graphs popup, or (2) roughly, by double clicking a graph focus marker and then moving it.

9.2 Overlaying Graphs

Overlaying one graph onto another is useful for creating a graph with two different x axes and/or y axes. For example, you may wish to have a graph which on the x axis has the month of the year. There could be 2 curves on it, one using the left y axis which is number of gnus sold and one using the right y-axis which is the number of gnats exported on a logarithmic scale. Likewise, if one is plotting spectral data, one could have one x axis in Hz and another one in wavelength. Let’s proceed with an example:data

1. Begin by selecting Main:Edit/Overlay graphs to bring up the Overlay widget.

2. Select the graph numbers with which we would like to deal. In this example, we will overlay graph 1 onto graph 0. At this point, only graph 0 is visible. We cannot see Graph 1 to select since it does not exist at this point. We need to create simply by pressing mouse button 3 in a graph list window and selecting create new.

3. The overlay type is determined by what is common among the overlayed graphs. In our example, the x axis is common so we will select X-axes same, Y-axes different. This is important because we don’t want to alter any axes of the Overlay graph which we set the same as the underlay graph. In this example, we don’t want to alter the x-axis of graph 1.

4. We are now ready to label the graph axes and read the data. One thing we must be careful to do is to always make sure that we are working on the intended graph. Seeing as the graphs are overlain, clicking within the frame is ambiguous as to what graph is selected. The rule is that in a region of overlay, clicking will cycle between the graphs. Hence, if graph 1 is selecting, clicking within the frame will toggle to graph 0.

5. Making sure that graph 0 is active, bring up the Axis properties widget. Now set the y axis title to Gnus.

6. Select graph 1 as active as set the title as Gnats. Notice how it overlaps the Gnus. We want to put this on the right side. From the axis label and bar tab, select label Properties/Side=Opposite.

7. Label the x axis to label it. If graph 1 is the current graph, noticed how it is greyed out because only 1 x axis need be active. Select graph 0 and you should now be able to alter the axis label.

8. You are ready to read in data. Just make sure the graph that is active when you read in the data (or create your set) is the one in which you intend it to go.

10 Hot Links

Hot links are a way of of updating a set without having to delete it first and then reread it. The Hot Links window is opened available under Main:Data/Hot links.

10.1 File containing a Single Set

The simplest hot link is to a file containing just one set. To make a hot link to a single set, we must first select the set we want to get updated and then specify the file. We may also link to a pipe in which case we must specify it is a pipe to which we are linking. A command may also be entered which will be run every time the hot link is updated. A common command might be autoscale which will make sure that the entire set can be seen if it changes size. It’s possible you may want to execute more commands than one. One could, for example, have a set that is a function of 2 sets that needs to be recomputed if either set is updated. If this is the case, put your commands in a file and then use the ”READ BATCH” command.

Pressing the Link button will now create the link and if the update button is pressed, the set will be updated with the current contents of the file you linked and the contents of the Command widget will be executed.

For a simple example, read in the set 10.1.dat and set up the hot link. Now, run the command shiftdata.sh and update the hotlink. You should have seen the peak in the graph shift. Try repeating this a couple of more times.

10.2 Multiple sets within a file

Sometimes a data file may contain multiple columns of data and we would like to be able to link to all or some of those columns. To specify this, select as many sets as there are xy columns of data in the file. The ”x y1 y2” format is assumed. Choose the file the data and link. Now in the link list, the links will show the file name with an appended colon and number. The number tells what column of data the link refers to. Any unwanted columns may be selected and unlinked at this point. When the update button is selected, all sets in the graph will be updated.

10.3 Updating by hot keys

Instead of having to keep the Hot links window open all the time, the update action is bound to alt-u. If you find that alt-u has no effect, try double clicking inside the graph you want to update and close the window that pops up. This will ”alert” the canvas to process future hot key strokes.